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Abstract Ultrawide‐bandgap semiconductors such as AlN, BN, and diamond hold tremendous promise for high‐efficiency deep‐ultraviolet optoelectronics and high‐power/frequency electronics, but their practical application has been limited by poor current conduction. Through a combined theoretical and experimental study, it is shown that a critical challenge can be addressed for AlN nanostructures by using N‐rich epitaxy. Under N‐rich conditions, the p‐type Al‐substitutional Mg‐dopant formation energy is significantly reduced by 2 eV, whereas the formation energy for N‐vacancy related compensating defects is increased by ≈3 eV, both of which are essential to achieve high hole concentrations of AlN. Detailed analysis of the current−voltage characteristics of AlN p‐i‐n diodes suggests that current conduction is dominated by hole‐carrier tunneling at room temperature, which is directly related to the activation energy of Mg dopants. At high Mg concentrations, the dispersion of Mg acceptor energy levels leads to drastically reduced activation energy for a portion of Mg dopants, evidenced by the small tunneling energy of 67 meV, which explains the efficient current conduction and the very small turn‐on voltage (≈5 V) for the diodes made of nanoscale AlN. This work shows that nanostructures can overcome the dopability challenges of ultrawide‐bandgap semiconductors and significantly increase the efficiency of devices.